Time : Three hours
1. Simplify the expression ((AB’ + ABC)’ + A (B + AB’))’.
2. Find the minimum expression of
Y= π (0,1,3,5,6,7,10,14,15).
3. Draw the full adder circuit as a collection of two half adder.
4. A circuit is to be designed that has one control line and three data lines. When the control line is high, the circuit is to detect when one of the data lines has a 1 on it. No more than one data line will ever have a 1 on it. When the control line is low, the circuit will output a 0, regardless of what is on the data lines.
5. The input frequency of a 7497 binary rate multiplier is 64 K Hz. What will its output be if the multiplier word is 1011?
6. Implement a digital circuit that statistics the following:
F (A, B, C, D) = ∑ (0,2,6, 7, 8, 10, 12)
10. Find a critical race free state assignment for the reduced flow table shown.
PART B - (5 x 16 80 marks)
11 (a) Reduce the expressioi using Quine McCluskey method.
F(x1,x2,x3,x4,x5)=∑m(0, 2,4,5,6,7,8,10,14,17,18,21,29,31) + ∑d (11, 20, 22)
12. (a) Design a combinational circuit that multiplies by 5 an input decimal digit represented in BCD. The output is also in BCD. Show that the outputs can be obtained from the input lines without using any logic gates.
FA,B,C,D)= ∑(1,3,4, 11, 12, 13, 14, 15).
if A = B and y= 1 if A < B and z=1 if A > B.
reduced state table.
(iii) Design a counter with the following repeated binary sequence: 0 1,3,5,7. UseT flipflops.
15. (a) A traffic light is installed at a junction of railroad and road. The traffic light is controlled by two switches in the rails placed one mut apart on either side of the junction. A switch is turned on when the train is over it and is turned off otherwise.The train light changes from green (logic -0) to red (logic - 1) when the beginning of the train is one mile from the junction. The light changes back to green when the end of the train is one mile away from the junction. Assume that the length of the train is less than two miles.
(ii) Show that the flow table can be reduced to four rows.
Y = x1x2'+(x1 ± x2')y
(ii) Derive the transition table and output map.
(iii) Obtain 2 state flow table.
(iv) Describe in words the behavior of the circuit.